If I die in another dimension, will the 5-minute clock start while I am in the overworld?
Solution 1:
No, the chunk needs to be loaded, which means it must be on the same dimensional plane and nearby.
Solution 2:
Minecraft items only are in danger of expiring when they are loaded into memory.
When you're in the overworld, the nether is not loaded (I'm assuming you're in single player?), so take all the time you need.